Ramin Takloo-Bighash : Minimal permutation representations of finite groups

Posted by , part of the Graduate Student Colloquium.

At

Feb. 15, 2008, 3 p.m.

In

SEO 636

Abstract

Let G be a finite group. A classical theorem of Cayley asserts that one can always find an injective homomorphism of G into a permutation group S_n. A minimal n for which such an injection exists is called the degree of G, and the associated homomorphism a minimal permutation representation. In this talk, after explaining a number of classical and new results about minimal representations, I will explain a new polynomial time algorithm to find minimal representations of a p-group given the subgroup lattice of the group - the naive algorithm is exponential time. I will end by describing some (surprising) applications of the algorithm to the structure theory of p-groups and a conjecture. This is joint with Ben Elias and Lior Silberman. The talk will be accessible to anyone with one semester of undergraduate algebra.